CN114638046A - Railway pier digital twin variable cross-section simulation calculation method - Google Patents
Railway pier digital twin variable cross-section simulation calculation method Download PDFInfo
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Abstract
The invention discloses a railway pier digital twin variable cross section simulation calculation method, which comprises the following steps of: inputting the overall section size information of the bridge pier; dividing the units and calculating corresponding contour information; digitizing the information of the two sections at the upper end and the lower end of each unit; calculating the geometric characteristics of each section; calculating a unit stiffness matrix of each pier unit; calculating the equivalent node load of each pier unit; forming an integral rigidity matrix and an integral load array of the pier. The method constructs a geometric characteristic calculation method of any section by self-defining an input format of any section and a finite element solution method based on a Poisson equation; a variable cross-section space beam unit rigidity matrix is deduced by a force balance and complementary energy theorem and a second Karschner theorem, equivalent node loads are obtained by a structural mechanics method, and then a variable cross-section space beam unit technology is established. The method accurately simulates the rigidity and the load of the digital twin simulation model and solves the problem of accuracy.
Description
Technical Field
The invention belongs to the technical field of bridge engineering in the traffic transportation industry, and particularly relates to a simulation calculation method for a digital twin variable cross section of a railway pier.
Background
By the end of 2021, the national operating mileage of high-speed railways reaches 4 kilometers, and by the end of 2025, a highway network with eight longitudinal and eight transverse frameworks as main frameworks covers over 50 million people, and the operating mileage of the high-speed railways reaches 5 kilometers. The proportion of the bridge structure in most high-speed rail lines is over 50%, and the design, construction and operation environment of the high-speed rail bridge is increasingly complex while the coverage area of a railway network is continuously enlarged. Under the influence of soft soil foundation settlement, train circulating live load, sunlight temperature difference, shrinkage and creep and the like, the piers can inevitably generate unrecoverable deformation and recoverable elastic deformation such as settlement, lateral deviation, displacement and the like to cause deterioration of the geometrical state of the track, so that disturbance is generated on a train running at high speed, and the higher the speed is, the larger the disturbance is, and the driving safety and the comfort level of passengers are seriously influenced.
In the design stage, the calculation accuracy of external force, deformation and the like of the pier foundation is improved by exerting force under the condition of fully considering all working conditions of construction, operation and maintenance, and the millimeter-scale smoothness of the track is better kept from the design angle.
During the calculation of the rigidity of the pier, the simplification processing is usually performed by adopting a segmental equal-section flexibility matrix method, for the variable-section pier, the calculation precision of the method depends on the density of segmental division, and the accuracy of the rigidity calculation influences the distribution of longitudinal force of the steel rail and the accuracy of a railway pier digital twin model.
Aiming at the problems, a set of railway pier digital twin variable cross-section simulation calculation method is needed to be researched for systematically solving the problem of accurately simulating the railway pier twin model in the real environment.
Disclosure of Invention
The invention is provided for solving the problems in the prior art, and aims to provide a digital twin variable cross section simulation calculation method for railway piers.
The technical scheme of the invention is as follows: a railway pier digital twin variable cross-section simulation calculation method comprises the following steps:
A. inputting the overall section size information of the bridge pier;
B. dividing the units and calculating corresponding contour information;
C. digitizing the information of the two sections at the upper end and the lower end of each unit;
D. calculating the geometric characteristics of each section;
E. calculating a unit stiffness matrix of each pier unit;
F. calculating the equivalent node load of each pier unit;
G. forming an integral rigidity matrix and an integral load array of the pier.
Further, the pier overall section size information input in the step A is obtained according to a railway pier entity, and the overall section size information comprises the height of the pier, the contour size of the bottom of the pier, the contour size of the top of the pier and the geometric transition form from the bottom of the pier to the top of the pier.
Further, the step B divides the cells and calculates the corresponding contour information, and the specific process is as follows:
firstly, segmenting the bridge pier along the height to obtain bridge pier units;
and then, calculating the height of each pier unit, the profile information of the cross sections of the upper end and the lower end and the change rule in the height range.
Furthermore, step C digitizes the information of the two sections at the upper and lower ends of each unit, and is implemented by a predefined arbitrary section input rule.
Further, step D calculates the geometric characteristics of each cross section by the following specific process:
firstly, carrying out grid division on each section;
then, the geometric characteristic value of each section is calculated by using a finite element calculation method of the Poisson equation.
Further, step E calculates a cell stiffness matrix of each pier cell, specifically including the following steps:
and (3) utilizing a variable cross-section rigidity matrix obtained by derivation based on a force balance equation, a complementary energy principle and a second Karschner theorem and solving the rigidity matrix of the pier unit.
Further, step F is to calculate the equivalent node load of each pier unit, and the specific process is as follows:
and calculating equivalent node load by using a transfer angular displacement equation in structural mechanics and a concrete expression of fixed end bending moment and fixed end shearing force corresponding to relevant working conditions in a matrix displacement method.
Further, the step G of forming the integral rigidity matrix and the integral load array of the pier comprises the following specific processes:
e, superposing the stiffness matrix corresponding to each pier unit obtained in the step E to the corresponding position of the overall stiffness matrix according to the corresponding coordinate position of the stiffness matrix in the overall coordinate system and the specific row number and column number of the stiffness matrix in the overall coordinate system, and integrating the overall stiffness matrix;
and F, superposing the equivalent node load corresponding to each pier unit obtained in the step F to the corresponding position of the whole load array according to the corresponding coordinate position of the equivalent node load in the whole coordinate system and the specific row and column numbers of the equivalent node load in the whole coordinate system, and integrating the whole load array. And finally, the twin information of the whole rigidity matrix and the whole load array required by simulation calculation is formed.
Furthermore, the arbitrary section input rule predefined in step C includes the edges input in the counterclockwise direction, and the edge interval numbers are arranged between the edges.
Furthermore, each side information is included in each side in the step C, the information of each side includes 5 parameters, and each parameter interval number is set between the parameters.
The invention has the following beneficial effects:
aiming at the problem of establishing a digital twin simulation model for a railway variable-section pier, a calculation method for geometrical characteristics of any section is constructed by self-defining an input format of any section and a finite element solving method based on a Poisson equation; a variable cross-section space beam unit rigidity matrix is deduced by a force balance and complementary energy theorem and a second Karschner theorem, equivalent node loads are obtained by a structural mechanics method, and then a variable cross-section space beam unit technology is established.
The method can accurately simulate the rigidity and the load of the digital twin simulation model of the equal-section and variable-section pier in the field of transportation, and solves the problem of accuracy of the digital twin model.
Drawings
FIG. 1 is a schematic flow chart of the steps of the present invention;
FIG. 2 is an arbitrary cross-sectional schematic view of the present invention;
FIG. 3 is a schematic view of a variable cross-section space beam unit of the present invention;
FIG. 4 is a schematic illustration of the Midas test model of the present invention;
FIG. 5 is a comparison of the seismic force calculations of the present invention and Midas (pier No. 1);
FIG. 6 is a comparison of the present invention and the bending moment calculations for Midas seismic force (pier No. 1).
Detailed Description
The present invention is described in detail below with reference to the accompanying drawings and examples:
as shown in fig. 1 to 6, a method for simulating and calculating a digital twin variable cross section of a railway pier comprises the following steps:
A. inputting the overall section size information of the bridge pier;
B. dividing the units and calculating corresponding contour information;
C. digitizing the information of the two sections at the upper end and the lower end of each unit;
D. calculating the geometric characteristics of each section;
E. calculating a unit stiffness matrix of each pier unit;
F. calculating the equivalent node load of each pier unit;
G. forming an integral rigidity matrix and an integral load array of the pier.
The information of the total section size of the pier input in the step A is obtained according to a railway pier entity, and the information of the total section size comprises the height of the pier, the contour size of the bottom of the pier, the contour size of the top of the pier and the geometric transition form from the bottom of the pier to the top of the pier.
Step B, dividing the units and calculating corresponding contour information, wherein the specific process is as follows:
firstly, segmenting the bridge pier along the height to obtain bridge pier units;
and then, calculating the height of each pier unit, the profile information of the cross sections of the upper end and the lower end and the change rule in the height range.
As shown in fig. 2, step C digitizes the information of the two sections at the upper and lower ends of each cell, and is implemented by a predefined arbitrary section input rule.
Step D, calculating the geometric characteristics of each section, wherein the specific process is as follows:
firstly, carrying out grid division on each section;
then, the geometric characteristic value of each section is calculated by using a finite element calculation method of the Poisson equation.
As shown in fig. 3, step E calculates a cell stiffness matrix of each pier cell, and the specific process is as follows:
and (3) utilizing a variable cross-section rigidity matrix obtained by derivation based on a force balance equation, a complementary energy principle and a second Karschner theorem and solving the rigidity matrix of the pier unit.
Step F, calculating the equivalent node load of each pier unit, wherein the specific process is as follows:
and calculating equivalent node load by using a transfer angular displacement equation in structural mechanics and a concrete expression of fixed end bending moment and fixed end shearing force corresponding to relevant working conditions in a matrix displacement method.
And G, forming a pier integral rigidity matrix and an integral load array, wherein the concrete process is as follows:
e, superposing the stiffness matrix corresponding to each pier unit obtained in the step E to the corresponding position of the overall stiffness matrix according to the corresponding coordinate position of the stiffness matrix in the overall coordinate system and the specific row number and column number of the stiffness matrix in the overall coordinate system, and integrating the overall stiffness matrix;
and F, superposing the equivalent node load corresponding to each pier unit obtained in the step F to the corresponding position of the whole load array according to the corresponding coordinate position of the equivalent node load in the whole coordinate system and the specific row and column numbers of the equivalent node load in the whole coordinate system, and integrating the whole load array. And finally, the twin information of the whole rigidity matrix and the whole load array required by simulation calculation is formed.
And C, inputting rules of any predefined section in the step C, wherein the rules comprise all sides input in a counterclockwise direction, and all side interval numbers are arranged among all sides.
And step C, each side information is included in each side, the information of each side comprises 5 parameters, and each parameter interval number is arranged between the parameters.
In step B, it is necessary to define a division scheme along the height of the pier, and the division scheme may be performed every 1 m. And positioning the specific positions of the upper and lower end sections of each pier unit according to the division scheme, and then calculating the profile information of each section according to the geometric transition form from the pier bottom to the pier top.
And step C, digitizing the section of each pier through a set of predefined arbitrary section input rules. The predefined arbitrary section input rule is as follows:
the first and the second sides are input in the anticlockwise direction and separated by a semicolon;
secondly, the information of each edge contains 5 parameters, and the middle part is separated by commas;
the physical meanings of the three and 5 parameters according to the left and right sequence are as follows:
section number, >0 outer contour, <0 inner contour;
starting end point x coordinate;
starting end point z coordinate;
radius r, =0 straight-line segment, >0 circular arc radius;
indicating arc, =0 whole circle, >0 minor arc, <0 major arc.
For example, for a square with a side length of 3, if the lower left corner of the square is placed at the origin and the two sides are parallel to the coordinate axes, the data given in table 1 can be used to represent the square according to the input rules.
TABLE 1 Square input data with side length of 3
For a bridge pier, the section information defined by the rule is input into the sections at both ends of each bridge pier unit.
And D, gridding each section, and calculating the geometric characteristic value of each section by using a numerical expression and a finite element calculation method based on the Poisson equation. The specific calculation formula is as follows:
cross sectional areaAThe numerical calculation formula of (2) is:
wherein the content of the first and second substances,Nethe number of the units is represented,Ngthe number of points of the integral is represented,
、 
representing the weighting coefficients of the cells.
The numerical calculation formula of the section moment of inertia is as follows:
wherein, the first and the second end of the pipe are connected with each other,I yy 、I zz 、I yz respectively showing cross-sectional windingsy-y、z-z、y-zThe cross-sectional moment of inertia of the shaft, ((ii))y 0, z 0) The coordinates of the centroid are represented and,y、zthe longitudinal and transverse coordinates of the cross-section are indicated, with the remaining symbols being as above.
The formula meaning of the conventional section characteristic calculation is definite, but the calculation of the torsion characteristic is relatively complex, and the calculation needs to be solved by a finite element solution method of a Poisson equation, wherein the solution process is as follows:
the torsional function of the section is expressed by omega, and the control equation can be obtained from the balance equation in the axial direction
Note:Arepresenting the cells within the cross-sectional profile.
At the outer boundary r of the cross-section0Above, the following boundary conditions are satisfied
Wherein the content of the first and second substances,n y 、n z indicating the directional cosine, the remaining symbols being as above.
Based on the control equation, the unit equivalent stiffness is obtainedK eAnd load right end termR e
Wherein, the first and the second end of the pipe are connected with each other,Na shape function vector representing a section division mesh of the pier element,Aeeach of the divided cells on the cross-section is shown,Tindicating a transpose operation on the matrix, with the remaining symbols being as above.
Substituting equation (5) into the cell balance equation (6) to obtain the cell twist functionω e
Note:K eandR erespectively a unit stiffness matrix and a unit equivalent node load vector based on the Poisson equation.
Then, the torsion constant can be calculated by using the following formulaJ
The same symbols are used as above.
After the section characteristics are obtained through calculation, when the rigidity or the internal force of the pier is calculated, only parameters corresponding to the sections at the two ends of the beam unit need to be given.
In the step E, a stiffness matrix of each pier unit needs to be solved, at this time, a required variable cross-section stiffness calculation formula needs to be derived by using a force-based equilibrium equation, a complementary energy principle and a second karman's theorem, and the calculation process is as follows:
the relationship between the node force and the node displacement of one end j of the unit is obtained by the static balance condition, the complementary energy theorem and the Kaplan theorem as follows:
whereinR j The integral format of the compliance matrix is expressed as:
（9）
wherein the content of the first and second substances,u j 、v j 、w j are respectively nodesjThe longitudinal, transverse and vertical horizontal node displacement,θ jx 、θ jy 、θ jz are respectively nodesjAngular displacements around three horizontal directions;N、Q y 、Q z respectively represent axial force and shearing force in two directions,TT、M y 、M z respectively representing torque, windingy、zBending moments, subscripts, in both directions of the axisjRepresentative nodej；E、GRespectively, an elastic modulus and a shear modulus,A(x)、I y (x) 、I z (x) The sectional area along the length direction of the beam and the rotational inertia around the two axes of y and z,J(x) In order to resist the torsional moment of inertia,Lin order to be the length of the unit,f sy 、f sz to account for the coefficients of the shear effect.
Compliance matrix of the pair (9)R j The inverse can obtain a corresponding rigidity matrixK jj 。
Establishing a rigidity matrix of the space variable cross-section beam unit, wherein the rigidity matrix has a relation formula:
wherein the content of the first and second substances,Frepresenting the nodal forces of a variable cross section beam element,δindicating node displacement.
For the left-constrained model, equation (10) can be simplified as:
from static equilibrium conditions
Can be recorded as
From formulas (10) and (11):
in the above-mentioned manner,TTin order to provide a torque of the variable cross-section beam unit,TT i is a beam unit with variable cross sectioniThe torque at the end of the shaft is,TT j is a beam unit with variable cross sectionjThe torque at the end of the shaft is,Ha first matrix representing the trailing edge of the medium sign of formula (12), synthesis (14) andK jj the rigidity matrix of the variable cross-section beam unit can be obtained by the expression of (1). The constant section rigidity matrix can be obtained through degeneration of the variable section rigidity matrix.
Therefore, the rigidity characteristic of each pier unit can be uniformly subjected to digital twin simulation by using the variable cross-section rigidity matrix.
In the step F, the influence on the node force is small due to the large rigidity and the change of the section form of the pier structure. When the node load of the unit is calculated, the equivalent node load of each pier unit can be calculated by adopting a structural mechanics transfer angular displacement equation and specific expressions such as fixed end bending moment, fixed end shearing force and the like corresponding to relevant working conditions in a matrix displacement method.
And G, superposing the variable cross-section rigidity matrix and the load array of each pier corresponding to all the units divided by the whole pier to the corresponding positions of the overall rigidity matrix and the overall load array according to the corresponding coordinate positions of the variable cross-section rigidity matrix and the load array in the overall coordinate system and the specific row numbers and column numbers of the variable cross-section rigidity matrix and the load array in the overall coordinate system, and integrating the overall rigidity matrix and the overall load array to finally form twin information required by simulation calculation.
Example one
The method is used for comparing and verifying the seismic force calculation results of the (60+100+60) m high-speed rail continuous beam.
Both the beam body and the pier are variable cross-section members, and the cross-sectional dimensions of the pier and the bearing platform are shown in table 2. Fig. 4 is a Midas model of a (60+100+60) m high-speed rail continuous beam, a self-programmed program is simulated and loaded by using the variable cross-section unit of the invention, and the cross-section geometric characteristics are calculated by using the arbitrary cross-section characteristic calculation function of the invention.
TABLE 2 model pier and bearing platform size table
In the testing process, five pier height combinations are formulated as testing working conditions 1-5, and the pier height combinations corresponding to the working conditions are shown in table 3.
Table 3 combination data table for testing pier height corresponding to five working conditions
And calculating values of longitudinal horizontal force and bending moment, transverse horizontal force and bending moment of the No. 1-4 pier corresponding to the five working conditions are calculated and extracted.
Figure 5 shows a longitudinal and transverse horizontal force comparison diagram of pier No. 1 under five working conditions,Px、Pyrepresenting MidasLongitudinal, transverse horizontal force, kN; Fx、Fyrepresenting longitudinal and transverse horizontal forces kN of the digital twin variable cross-section simulation calculation method of the pier.
Figure 6 shows a comparison of the longitudinal and transverse bending moments of pier No. 1,Mx、Myrepresents the longitudinal and transverse bending moments of Midas, kN m;FFx、FFyrepresenting the longitudinal and transverse bending moments kN m of the digital twin variable cross section simulation calculation method of the pier.
Table 4 shows the specific values of each calculation parameter of pier No. 1, the corresponding digital twin variable cross-section simulation calculation method for the pier and the error values of Midas under the five pier height combination working conditions.
As can be seen from the comparison graphs and the comparison tables given in fig. 5, fig. 6 and table 4, the digital twin variable cross-section simulation calculation method for piers is very close to the calculated value of Midas, and the maximum error is 0.18%.
TABLE 4 comparison table of earthquake force and earthquake bending moment under various earthquake conditions (pier No. 1)
Table 5 shows the error values for piers No. 2-4, and it can be seen that the maximum error is 0.15%. The seismic force calculation relates to solving of vibration mode frequency and is related to the rigidity and mass matrix of the variable cross-section beam, so that the digital twin variable cross-section simulation calculation method for the bridge pier meets the digital twin simulation requirement of actual engineering.
TABLE 5 (2-4) TABLE for summary of errors of simulation calculation method for Midas and pier digital twin variable cross-section of pier
Aiming at the problem of establishing a digital twin simulation model for a railway variable-section pier, a calculation method for geometric characteristics of any section is constructed by self-defining an input format of any section and a finite element solving method based on a Poisson equation; a variable cross-section space beam unit rigidity matrix is deduced by a force balance and complementary energy theorem and a second Karschner theorem, equivalent node loads are obtained by a structural mechanics method, and then a variable cross-section space beam unit technology is established.
The method can accurately simulate the rigidity and the load of the digital twin simulation model of the equal-section and variable-section pier in the field of transportation, and solves the problem of accuracy of the digital twin model.
Claims (10)
1. A railway pier digital twin variable cross-section simulation calculation method is characterized by comprising the following steps: the method comprises the following steps:
(A) inputting the overall section size information of the bridge pier;
(B) dividing the units and calculating corresponding contour information;
(C) digitizing the information of the two sections at the upper end and the lower end of each unit;
(D) calculating the geometric characteristics of each section;
(E) calculating a unit stiffness matrix of each pier unit;
(F) calculating the equivalent node load of each pier unit;
(G) forming an integral rigidity matrix and an integral load array of the pier.
2. The railway pier digital twin variable cross-section simulation calculation method according to claim 1, characterized in that: and (C) the total section size information of the piers input in the step (A) is obtained according to the railway pier entity, and the total section size information comprises the height of the piers, the contour size of the bottom of the piers, the contour size of the top of the piers and the geometric transition form from the bottom of the piers to the top of the piers.
3. The railway pier digital twin variable cross-section simulation calculation method according to claim 1, characterized in that: dividing the unit and calculating corresponding contour information in the step (B), wherein the specific process is as follows:
firstly, segmenting the bridge pier along the height to obtain bridge pier units;
and then, calculating the height of each pier unit, the profile information of the cross sections of the upper end and the lower end and the change rule in the height range.
4. The railway pier digital twin variable cross-section simulation calculation method according to claim 1, characterized in that: and (C) digitizing the information of the two sections at the upper end and the lower end of each unit, and realizing through a predefined arbitrary section input rule.
5. The railway pier digital twin variable cross-section simulation calculation method according to claim 1, characterized by comprising the following steps of: step (D) calculating the geometric characteristics of each section, wherein the specific process is as follows:
firstly, carrying out grid division on each section;
then, the geometrical characteristic value of each section is calculated by using a finite element calculation method of Poisson equation.
6. The railway pier digital twin variable cross-section simulation calculation method according to claim 1, characterized in that: calculating a unit stiffness matrix of each pier unit, wherein the specific process is as follows:
and (3) utilizing a variable cross-section rigidity matrix obtained by derivation based on a force balance equation, a complementary energy principle and a second Karschner theorem and solving the rigidity matrix of the pier unit.
7. The railway pier digital twin variable cross-section simulation calculation method according to claim 1, characterized in that: calculating the equivalent node load of each pier unit in the step (F), wherein the specific process is as follows:
and calculating equivalent node load by using a transfer angular displacement equation in structural mechanics and a concrete expression of fixed end bending moment and fixed end shearing force corresponding to relevant working conditions in a matrix displacement method.
8. The railway pier digital twin variable cross-section simulation calculation method according to claim 1, characterized in that: step (G) forms the integral rigidity matrix and the integral load array of the pier, and the concrete process is as follows:
superposing the stiffness matrix corresponding to each pier unit obtained in the step (E) to the corresponding position of the overall stiffness matrix according to the corresponding coordinate position of the stiffness matrix in the overall coordinate system and the specific row number and column number of the stiffness matrix in the overall coordinate system, and integrating the overall stiffness matrix;
superposing the equivalent node load corresponding to each pier unit obtained in the step (F) to the corresponding position of the whole load array according to the corresponding coordinate position of the equivalent node load in the whole coordinate system and the specific row and column numbers of the equivalent node load in the whole coordinate system to integrate the whole load array,
and finally, the twin information of the whole rigidity matrix and the whole load array required by simulation calculation is formed.
9. The railway pier digital twin variable cross-section simulation calculation method according to claim 4, characterized in that: and (C) inputting rules of any predefined section in the step (C), wherein the rules comprise all sides input in the anticlockwise direction, and all side interval numbers are arranged among all sides.
10. The railway pier digital twin variable cross-section simulation calculation method of claim 9, wherein: and (C) each side comprises information of each side, the information of each side comprises 5 parameters, and each parameter interval number is arranged between the parameters.
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| CN117951771A (en) * | 2023-11-29 | 2024-04-30 | 中铁五局集团电务工程有限责任公司 | Method for rapidly determining position of construction support of continuous steel box girder bridge oriented to optimal stress |
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